A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?

Ratios and Dilutions

Stage: 4 Challenge Level:

Why do this problem?

This problem provides a context within which to explore fractions and proportionality. Seeking concentrations which can be made in different ways and justifying why some concentrations can't be made at all gives practice on working with equivalent fractions, ratios, factors and multiples.

Possible approach

Begin by introducing the idea of a solution with strength 100000 cells/ml. Make sure everyone is clear about what this means.

Then ask the class to imagine mixing 100ml of this solution with 100ml of pure water. Students could record any working out and their answer on individual whiteboards. Now show students the interactivity, and use it to check their answer. Take time to discuss how they got to the correct answer.

Demonstrate that the interactivity can measure multiples of 10ml of liquid, up to 100ml - the scientific context of this could be using a dropper that measures 10ml at a time.

Ask students to come up with questions they would like to explore using the interactivity - some suggested questions appear in the problem. Then allow them some time to investigate, using the interactivity to check the predictions that they make.

Once students are competent at working with solutions created using one dilution, show them the second interactivity, which performs two dilutions. Perhaps start by giving them a couple of concentrations to work out, using individual whiteboards as before, and using the interactivity to check. At the end of the problem there are some suggested
concentrations they could be asked to make.

Pairs of students could take it in turns to create a concentration using two dilutions, and then challenge their partner to work out the dilutions they used.

Finally, the problem challenges students to investigate impossible dilutions.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.